Four years of IMP 8 magnetic field measurements, 1978--1982, when ISEE 3 took upstream interplanetary magnetic field (IMF) measurements, have been analyzed to produce full cross-section magnetic maps of the magnetotail at about 33RE downwind from Earth. This paper describes how the field geometry in the cross-sectional plane responds to different IMF orientations: dominant By, dominant +Bz, and dominant -Bz. The dominant By case exhibits marked departures from bilateral symmetry that have the sense of superimposing a fraction of the IMF on the symmetrical tail field. However, the ''superimposed'' perturbation field, measured as a fraction of the IMF, is highly nonuniform: It is maximum in the flanks of the plasma sheet and minimum in the lobes. There is also a rotation of the current sheet which varies with IMF strength and with distance. The two dominant Bz cases show no systematic departures from bilateral symmetry. However, the shapes and the relative sizes of the dipolar and flaring field regions of their cross sections are markedly different. The difference field, obtained by subtracting the positive Bz case from the negative Bz case, shows that the strongest perturbations run the north-south extent of the flanks, instead of residing in the lobes, as might be expected from the dayside reconnection model. ¿ American Geophysical Union 1994